On higher Brézin-Gross-Witten tau-functions

Alexandrov, Alexander; Dhara, Saswati

On higher Brézin-Gross-Witten tau-functions

Alexander Alexandrov
(
- POSTECH
)
,
Saswati Dhara
(
- POSTECH, Pohang
)

Apr 26, 2022

34 pages

e-Print:

2204.12273 [math-ph]

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Abstract: (arXiv)

In this paper, we consider the higher Brézin--Gross--Witten tau-functions, given by the matrix integrals. For these tau-functions we construct the canonical Kac--Schwarz operators, quantum spectral curves, and

W^{(3)}

-constraints. For the simplest representative we construct the cut-and-join operators, which describe the algebraic version of the topological recursion. We also investigate a one-parametric generalization of the higher Brézin--Gross--Witten tau-functions.

Note:

34 pages

tau-functions
KP hierarchy
W-constraints
BGW tau-function
cut-and-join operator
enumerative geometry
moduli spaces
tau-function
Kadomtsev-Petviashvili equation: hierarchy
matrix model

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